Slanted sides of a tent are 11 feet long each and the bottom of the tent is 12 feet across. what is the tallest point of the tent?

You have a right angled triangle made up of a 11 foot hypotenuse and a base of 6 feet (the tent pole would be in the middle of 12 feet).

Call the height of the tent pole x

Use Pythagoras. The square on the hypotenuse = sum of squares on the other two sides:
x^2 + 6^2 = 11^2
x^2 + 36 = 121
x^2 = 85
x = 9.22 feet